Having lived in the neighborhood for a couple of years and being a pizza fanatic, I would rank things in the following order:
1) La Gondola (Ashland; their Belmont location is distinctly sub-par in comparison) – The best Chicago-style thin-crust in the neighborhood.
2) Dimo's (formerly Ian's) – Same owner, same kind service, same free pepperoni, same almost New York-style pizza with a deliciously sweet sauce and tons or weird topping blends.
3) Art of Pizza – Mainly known for their great stuffed pizza, their thin crust is also quite good.
4) Cafe Luigi – Formerly the best NYC-style pizza in Chicago, they've now been eclipsed by several other places (i.e. Armitage Pizzeria, in Lincoln Park and no delivery but by far the best East Coast pizza place in Chicagoland). Their best is still great, but it's not often that they serve that up. Even their bad nights are still quite tasty, though.
5) Pat's Pizza (also a Lincoln Park spot) – This might be controversial, but I've never understood the love this place gets. I heard from many people when I moved here that this was THE spot for Chicago thin-crust on the north side. Not a fan. It's not bad, it's just mediocre.
6) D'Agostino's – Really solid. Perfect for delivery when you've come home trashed from watching football at the bar and you're too tired to make something.
7) Mista – Hate, hate, hate this place. Crust is a joke as matzoh is tastier and has more flavor than their crust. Claims to have high quality ingredients, but "fresh" mozzarella does not make a good pizza if it's of poor quality. I'd take an aged low-moisture mozz over whatever Mista uses any day of the week. They don't really have a "sauce" so to speak, they seem to just marinate their tomatoes in some balsamic-based concoction. I know I'm an outlier here, but I can't figure out what is good about this place.
Never had Pie Hole or Panino's.